Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×Dic428 | C2 | semidirect |
| 3. #20293070 | C2 | direct (N × H) |
| 4. C2×Dic856 | C2 | semidirect |
| 5. C2×#16812054 | C2 | semidirect |
| 6. C2×M32×C107 | C2 | semidirect |
| 15. C2×Dic428 | C22 | semidirect |
| 18. Dic856 | C22 | semidirect |
| 19. #16812054 | C22 | semidirect |
| 21. M32×C107 | C22 | semidirect |
| 80. C2×C107 | #510 | semidirect |
| 84. C107 | C2×#510 | semidirect |
| 90. C2×M32 | D107 | semidirect |
| 105. M32 | C2×D107 | semidirect |
| 165. C2 | #20293070 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812131 | 2 |
| C22×Dic428 | 2 |
| #20293070 | 2 |
| C2×Dic856 | 2 |
| C2×#16812054 | 2 |
| C2×M32×C107 | 2 |
| C2×#510 | 107 |